polarRLCE: A New Code-Based Cryptosystem Using Polar Codes

Abstract

Security challenges brought about by the upcoming 5G era should be taken seriously. Code-based cryptography leverages difficult problems in coding theory and is one of the main techniques enabling cryptographic primitives in the postquantum scenario. In this work, we propose the first efficient secure scheme based on polar codes (i.e., polarRLCE) which is inspired by the RLCE scheme, a candidate for the NIST postquantum cryptography standardization in the first round. In addition to avoiding some weaknesses of the RLCE scheme, we show that, with the proper choice of parameters, using polar codes, it is possible to design an encryption scheme to achieve the intended security level while retaining a reasonably small public key size. In addition, we also present a KEM version of the polarRLCE scheme that can attain a negligible decryption failure rate within the corresponding security parameters. It is shown that our proposal enjoys an apparent advantage to decrease the public key size, especially on the high-security level.

An Optimized Method for Polar Code Construction

“…The previous approaches of polar codes construction require one to one compute of the reliability for all synthetic channels and use only those that are sufficiently reliable [2]. For the gain in complexity and resources, it is worthwhile to perform an optimized construction polar codes algorithm.…”

“…The polar codes proposed by Arikan in 2008 can achieve that capacity of any binary discrete memoryless channel [1], researchers from all over the world have been interested in polar codes ever since their introduction in [1], polar codes can be used in lot of applications like cryptgraphy [2], speech communication [3], data storage [4]. Polar codes are also used to develop new block [5].…”

A Novel Niederreiter-like cryptosystem based on the (u|u + υ)-construction codes

“…The scheme is a new variant of the Niederreiter-PKE scheme which we recall it in Section 2.5. We respect here the generator matrix of the (u|u + v)−construction code and we use the technique of adding random column scrambler in the parity check matrix of the code [21].…”

Software implementation of systematic polar encoding based PKC-SPE cryptosystem for quantum cybersecurity

“…Therefore, it is crucial to find techniques to decrease key sizes for this cryptosystem while maintaining the optimum level of security. Following the origin of this cryptosystem, researchers have proposed other variations based on error-correcting codes, including the Reed-Solomon 7 , Reed-Muller, Turbo 8 , 9 , and Cyclic codes. However, the majority of these variations are broken 10 or have some flaws 11 , 12 associated with them.…”

“…By preserving these bits, error detection and correction can be improved, resulting in a lower Bit Error Rate (BER) 15 .The recursive nature of polar codes makes them suitable for real-time communication systems, cryptographic protocols, and storage technologies. As a result, polar codes are more practical for real-world applications because of their systematic nature, making a significant contribution to coding theory and cryptography 7 . In recent years, many variants 10 , 11 , 16 , 17 of the McEliece encryption scheme based on polar codes have been addressed by several researchers.…”